Hi,
For replacing the result URL (or parts of it), I would rather recommend using the asp_results hook, here is this example.
For post type results, you can use the advanced title and content fields to display taxonomy terms in the result content or title fields.
I would recommend using a custom CSS to remove the overlay. There is an option, but the node still remains there, so use this if you want to make sure:
.asp_r span.overlap {
display: none !important;
}